// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2013 Christoph Hertzberg <chtz@informatik.uni-bremen.de>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <unsupported/Eigen/AutoDiff>

/*
 * In this file scalar derivations are tested for correctness.
 * TODO add more tests!
 */

template<typename Scalar>
void
check_atan2()
{
	typedef Matrix<Scalar, 1, 1> Deriv1;
	typedef AutoDiffScalar<Deriv1> AD;

	AD x(internal::random<Scalar>(-3.0, 3.0), Deriv1::UnitX());

	using std::exp;
	Scalar r = exp(internal::random<Scalar>(-10, 10));

	AD s = sin(x), c = cos(x);
	AD res = atan2(r * s, r * c);

	VERIFY_IS_APPROX(res.value(), x.value());
	VERIFY_IS_APPROX(res.derivatives(), x.derivatives());

	res = atan2(r * s + 0, r * c + 0);
	VERIFY_IS_APPROX(res.value(), x.value());
	VERIFY_IS_APPROX(res.derivatives(), x.derivatives());
}

template<typename Scalar>
void
check_hyperbolic_functions()
{
	using std::cosh;
	using std::sinh;
	using std::tanh;
	typedef Matrix<Scalar, 1, 1> Deriv1;
	typedef AutoDiffScalar<Deriv1> AD;
	Deriv1 p = Deriv1::Random();
	AD val(p.x(), Deriv1::UnitX());

	Scalar cosh_px = std::cosh(p.x());
	AD res1 = tanh(val);
	VERIFY_IS_APPROX(res1.value(), std::tanh(p.x()));
	VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(1.0) / (cosh_px * cosh_px));

	AD res2 = sinh(val);
	VERIFY_IS_APPROX(res2.value(), std::sinh(p.x()));
	VERIFY_IS_APPROX(res2.derivatives().x(), cosh_px);

	AD res3 = cosh(val);
	VERIFY_IS_APPROX(res3.value(), cosh_px);
	VERIFY_IS_APPROX(res3.derivatives().x(), std::sinh(p.x()));

	// Check constant values.
	const Scalar sample_point = Scalar(1) / Scalar(3);
	val = AD(sample_point, Deriv1::UnitX());
	res1 = tanh(val);
	VERIFY_IS_APPROX(res1.derivatives().x(), Scalar(0.896629559604914));

	res2 = sinh(val);
	VERIFY_IS_APPROX(res2.derivatives().x(), Scalar(1.056071867829939));

	res3 = cosh(val);
	VERIFY_IS_APPROX(res3.derivatives().x(), Scalar(0.339540557256150));
}

template<typename Scalar>
void
check_limits_specialization()
{
	typedef Eigen::Matrix<Scalar, 1, 1> Deriv;
	typedef Eigen::AutoDiffScalar<Deriv> AD;

	typedef std::numeric_limits<AD> A;
	typedef std::numeric_limits<Scalar> B;

	// workaround "unused typedef" warning:
	VERIFY(!bool(internal::is_same<B, A>::value));

#if EIGEN_HAS_CXX11
	VERIFY(bool(std::is_base_of<B, A>::value));
#endif
}

EIGEN_DECLARE_TEST(autodiff_scalar)
{
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(check_atan2<float>());
		CALL_SUBTEST_2(check_atan2<double>());
		CALL_SUBTEST_3(check_hyperbolic_functions<float>());
		CALL_SUBTEST_4(check_hyperbolic_functions<double>());
		CALL_SUBTEST_5(check_limits_specialization<double>());
	}
}
